complement

In Grade VI, while studying about set theory, we come across different types of sets. Here we are going to define complement of a set.
If we say that U is the universal set and A is any set, which is the subset of set  U, then the complement of set A will be all the elements which belong to set  U but  does not belong to set A.  Complement of set A can be written as U – A. We express complement of set A as A’.  Thus we can say that
 A’ = U – A
 Also we can say that the elements of set A and the elements of set A’ ( which is the complement of set A, when U is the universal set ) join together to form the universal set  U. mathematically it can be expressed as follows: A  + A’ = U
It will be more clear by the following example: Let U = 1, 2, 3, 4 , 5, 6, 7, 8 , 9, 10 we say that set U is the universal set which represents the natural numbers from 1 to 10. Also let the  set A = 1, 3, 5, 7, 9 which is the set of all odd numbers from 1 to 10. (know more about free download cbse books, here)
 Now A’ = U – A
= 1, 2, 3, 4 , 5, 6, 7, 8 , 9, 10 -   1, 3, 5, 7, 9  = 2, 4, 6, 8, 10
 SO we observe that it will contain all the elements of the universal set U, which are not in A. Also if we add together set A and set A’ , then the resultant set will be the universal set itself.
Another important thing about  a complement is  that  a complement of any complement is the original set itself. It means: ( A’)’ = A
In the next session we will discuss about Possible outcomes.